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MODELING AND VALIDATION OF DAMPED PLEXIGLAS WINDOWS 

FOR NOISE CONTROL 


Ralph D. Buehrle*, Gary P. Gibbs*, Jacob Klos*, and Marina Mazurt 
NASA Langley Research Center 
Hampton, Virginia 23681 


Abstract 

Windows are a significant path for structure-borne 
and air-borne noise transmission in general 
aviation aircraft. In this paper, numerical and 
experimental results are used to evaluate damped 
plexiglas windows for the reduction of structure- 
borne and air-borne noise transmitted into the 
interior of an aircraft. In contrast to conventional 
homogeneous windows, the damped plexiglas 
windows were fabricated using two or three layers 
of plexiglas with transparent viscoelastic damping 
material sandwiched between the layers. 
Transmission loss and radiated sound power 
measurements were used to compare different 
layups of the damped plexiglas windows with 
uniform windows of the same nominal thickness. 
This vibro-acoustic test data was also used for the 
verification and validation of finite element and 
boundary element models of the damped plexiglas 
windows. Numerical models are presented for the 
prediction of radiated sound power for a point 
force excitation and transmission loss for diffuse 
acoustic excitation. Radiated sound power and 
transmission loss predictions are in good 
agreement with experimental data. Once 
validated, the numerical models were used to 
perform a parametric study to determine the 
optimum configuration of the damped plexiglas 
windows for reducing the radiated sound power for 
a point force excitation. 

Introduction 

Laminated glass has been shown to provide 
benefits for noise reduction in automotive and 
architectural applications. 1 4 Recent experimental 
work by Gibbs et. al. 5 shows the potential benefits 
of damped plexiglas windows based on 
comparisons of transmission loss and radiated 
sound power. The damped plexiglas windows 
were evaluated as replacements for conventional 
solid aircraft windows to reduce the structure- 
borne and air-borne noise transmitted into the 


*Aerospace Engineer, Structural Acoustics Branch 
+Cooperative Education Student, Purdue University 
This material is declared a work of the U.S. Government and is 
not subject to copyright protection in the United States. 


interior of general aviation aircraft. The damped 
plexiglas windows were fabricated using two or 
three layers of plexiglas with transparent 
viscoelastic damping material sandwiched 
between the layers as shown in Figure 1. For 
windows that were nominally V4” thick, reductions 
in the radiated sound power as large as 3.7 dB 
over a 1000 Hz bandwidth were shown 
experimentally when comparing damped and 
uniform windows. An increase in transmission 
loss of up to 4.5 dB over a 50 to 4000Hz 
frequency range was also shown. 

This work extends the plexiglas window study 5 to 
include finite element and boundary element 
modeling of the windows. Vibro-acoustic 
predictions were compared with vibration and 
acoustic response measurements for the windows 
installed in the NASA Langley Structural Acoustic 
Loads and Transmission (SALT) Facility. 6 Good 
agreement between measurement and predictions 
were obtained. Comparisons between the 
numerical and experimental data validate the 
numerical modeling approach. Using the validated 
numerical models, a parametric study was used to 
examine the optimum layup of the damped 
plexiglas windows. The test facility, hardware, 
vibro-acoustic tests, and numerical models are 
described. 

Test Facility 

The Structural Acoustic Loads and Transmission 
(SALT) Facility 6 located at the NASA Langley 
Research Center is shown in Figure 2. The SALT 
facility consists of an anechoic chamber, a 
reverberation chamber, and a shared transmission 
loss (TL) window. The anechoic chamber has a 
volume of 11,900 cubic feet (337 cubic meters). 
Interior dimensions of the anechoic chamber, 
measured from wedge tip to wedge tip, are 15 feet 
(4.57 meters) in height, 25 feet (7.65 meters) in 
width, and 32 feet (9.63 meters) in length. The 
reverberation chamber has dimensions of 14.8 
feet (4.5 meters) in height, 21.3 feet (6.5 meters) 
in width, and 31.2 feet (9.5 meters) in length for a 
volume of 9,817 cubic feet (278 cubic meters). A 
shared TL window accommodates test structures 
of up to 54- by 54-inches (1 .41 - by 1 .41 -meters). 


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Hardware Description 

A plexiglas window is shown installed in the SALT 
Facility in Figure 3. The SALT facility was setup 
as a transmission loss suite. A 48- by 24-inch 
plexiglas window was clamped between two 0.75- 
inch thick aluminum frames to approximate a fixed 
boundary condition. After mounting in the frame, 
the exposed portion of the plexiglas window 
measured 37.75- by 15.25-inches. The frame 
assembly was installed in a 3-inch thick fixture 
composed of medium density fiberboard, which 
was mounted in the transmission loss (TL) 
window. 


Radiated Sound Power 

A plexiglas window was mounted in the TL window 
of the SALT facility and excited with psuedo 
random excitation by a shaker. The spatial 
intensity was measured 7 with two-microphone 
intensity probes and the data was integrated over 
the measurement surface to obtain the radiated 
sound power. Figure 4 shows the results for 
several of the tested Vi-inch windows. The 
damped panels are shown to reduce the radiated 
sound power by up to 8 dB at some of the lower 
resonance frequencies and up to 3.7 dB over the 
1000Hz bandwidth. 


Table 1. Nominally Vi -Inch Test Windows 


Window 

Configuration 

Overall 

Thickness 

(inch) 

Weight of 
Exposed Panel 
(lbs) 

216 

0.216 

5.38 

114,2,114 

0.230 

5.72 

175,2,60 

0.237 

5.90 

30,2,175,2,30 

0.239 

5.94 

60,2,114,2,60 

0.238 

5.91 


The numerical studies will focus on a set of 
nominally Vi -inch thick windows. This set consists 
of a uniform window and four different layups of 
damped plexiglas windows. Table 1 provides a list 
of the layups for the windows. The thickness 
dimensions are in thousandths of an inch. For 
example, the 175,2,60 window has a 0.175-inch 
thick plexiglas layer, a 0.002-inch thick visoelastic 
layer, and a 0.060-inch thick plexiglas layer. All 
damped window test configurations used a .002- 
inch thick 3M™ viscoelastic damping polymer 
(Product No. 1 1 2P02). Due to the thickness of the 
available plexiglas sheets, overall window 
thickness and corresponding window weight 
varied by approximately ten percent. The weight 
estimates are based on the exposed portion of the 
window (37.75- by 15.25-inches) and 
manufacturer provided density values. For this 
study, the windows were all manufactured flat for 
ease of fabrication and testing. 

Vibro-Acoustic Tests 

Measurements of the radiated sound power and 
transmission loss of the damped and undamped 
plexiglas windows were made by Gibbs et.al. A 
brief summary of the setup and results are 
provided below. 


Transmission Loss 

The SALT facility was setup as a transmission loss 
suite with the reverberation chamber on the 
source side of the window and the anechoic 
chamber on the receiver side. The reverberation 
room was driven with four speakers, each directed 
into a corner, to produce a diffuse acoustic 
excitation of the window. The transmission loss 
was found from measurements of the incident and 
transmitted sound power. 7 

The transmission loss of the 216 window and the 
60,2,114,2,60 window are shown in Figure 5. The 
damped window shows a significant increase in 
the transmission loss at the resonance dip (80 Hz) 
and in the mass controlled region. This results in 
a 4.5 dB increase in transmission loss over a 50 to 
4000Hz frequency range. For a homogeneous 
panel, 8 the most significant improvement due to 
the addition of damping is expected at the lower 
resonant frequencies and above the coincident 
frequency. For the nominally Vi-inch thick 
plexiglas window the coincident frequency is 
approximately 6 kHz. As shown in figure 5, an 
increase in transmission loss of 6 dB is observed 
at and above coincidence, and at resonance. 

Vibroacoustic Test Summary 

The addition of a constrained viscoelastic damping 
layer provided a significant improvement in 
acoustic performance for the Vi-inch thick 
windows. 5 The 60,2,114,2,60 window resulted in 
the best acoustical performance of the windows 
tested. However, the question of the optimum 
layup remained. It was desirable to develop and 
validate methods to predict the observed change 
in radiated sound power and transmission loss 
due to the incorporation of constrained layer 
damping in the plexiglas windows. This led to the 
numerical studies described in the remaining 
sections. 


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Numerical Models 
Finite Element Model 

MSC.Nastran 2001 was used for the finite element 
analyses. The viscoelastic layer was modeled 
with eight node solid elements with isotropic 
material properties. Plate (CQUAD4) and solid 
elements (CHEXA) were evaluated for the 
plexiglas base and constraining layers. 
Comparisons of the models and a discussion of 
required mesh will be provided in the results. 
Isotropic material properties were assumed for the 
plexiglas. 

The material properties provided by the 
manufacturer for the plexiglas and viscoelastic 
damping material are listed in Table 2. Estimates 
of the damping properties of the plexiglas were 
based on comparisons with experimental results 
for the uniform window. The loss factor for both 
materials was entered as structural element 
damping (GE) on the material card of the finite 
element model. The viscoelastic damping material 
has frequency and temperature dependent 
properties. An ambient temperature of 20 degrees 
Celsius was assumed. 


Table 2. Material Properties 


Material 

Poisson 

Ratio 

Density 

lb-s 2 /in 3 4 

Shear 

Modulus 

psi 

Loss 

Factor 

Plexiglas 

0.35 

1.12e-4 

246000 

.07 

Viscoealstic 
(100 Hz) 

0.49 

9.36e-5 

362 

1 

Vicsoelastic 
(300 Hz) 

0.49 

9.36e-5 

725 

.85 

Viscoelastic 
(500 Hz) 

0.49 

9.36e-5 

1015 

.7 

Viscoelastic 
(1000 Hz) 

0.49 

9.36e-5 

1305 

.6 


A modal frequency response solution that included 
200 modes, up to a frequency of over 4000 Hz, 
was used to predict the response to unit force 
excitation over the 60 to 1000 Hz range. As noted 
previously, the viscoelastic material had frequency 
dependent material properties. The modal 
frequency response solution does not allow for 
frequency dependent material properties, so 
predictions are based on constant viscoelastic 
material properties corresponding to the values at 
100Hz. Incorporation of frequency dependent 
material properties requires the direct frequency 
response solution but this significantly increases 
computation time. As will be shown in the results 
section, the modal solution provided predictions 


consistent with the measured results. For each of 
the window layups, surface velocities were 
predicted for a given excitation and used as 
boundary condition input to the boundary element 
model. 

Boundary Element Model 

The boundary element model was developed in 
COMET/Acoustics. A grid of 39 elements along 
the length by 16 elements along the width was 
used to obtain adequate spatial resolution of the 
structural mode shapes through 1000 Hertz. A 
symmetric boundary was used to simulate the 
acoustic radiation of the baffled window into the 
anechoic chamber. The direct exterior boundary 
element analysis was used to predict the radiated 
sound power from imposed surface velocity data. 
Surface velocity data was based on finite element 
analyses with point force excitation and also the 
diffuse acoustic excitation. In order to evaluate 
the numerical data, the finite element velocity 
predictions were first interpolated to the reduced 
mesh size of the boundary element model and 
then analyzed. 

Diffuse Acoustic Excitation Model 

The finite element models of the 216 window and 
the 60,2,1 14,2,60 window were used to predict the 
change in the sound power transmission loss due 
to the addition of constrained layer damping. To 
use the finite element models to predict the 
transmission loss, a simulation of the excitation 
mechanism present in the experiment is needed. 

A diffuse acoustic excitation of the finite element 
models was developed based on plane wave 
propagation. A large number, N , of plane waves 
having random angles of incidence, random 
magnitudes, and random temporal phase angles 
were summed together to simulate a diffuse field 
excitation. A plane wave incident on the surface 
of a window at angles G n and y/ n is shown in Figure 
7. The angles 9 n and y/ n are uniformly distributed 
random numbers on the intervals [0,rc] and [0,2 n\ 
respectively and represent the angles of 
propagation in spherical coordinates. The n th 
plane wave has a magnitude of P n cos(6> n ), where 
P n is a uniformly distributed random number on the 
interval [0,1]. Thus the steady state pressure can 
be described in space and time by the equation 

P„ ( x , y, z, t ) = P n cos(0„ )e ~ ^ ** V (fl * + ' <*" > (1 ) 

where co is the angular frequency, <p n is a random 
temporal phase angle uniformly distributed on the 


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interval of [0,2n], and k x , k y and k z are the 
wavenumber in the x, y and z directions, 
respectively, found from 


The incident sound power is computed from the 
intensity vector of each of the N plane waves. The 
intensity vector, /„ , of the n th plane wave is 


k x = ksm(6 n )cos(l// n ) 

(2a) 

k Y = k sin (O n ) sin(^„ ) 

(2b) 

k , =kcos(0 n ) 

(2c) 


where k is the wavenumber in air at a particular 
analysis frequency. The random temporal phase 
angle is introduced to prevent the N plane waves 
from having the same phase angle at the origin. A 
weighting function of cos(0 n ) is included in the 
pressure magnitude to correct for the probability 
distribution of incident plane waves likely present 
in the experimental excitation. 9 The random 
variables 0 n , y/ n , P n and <f> n are unique for each of 
the N plane waves. Assuming steady state simple 
harmonic motion and a nearly rigid boundary 
condition at the surface of the window, the spatial 
pressure distribution exciting the window can be 
approximated by 


j(x, y,z,a>) = 2P n cos(9 n )e'0" e ^x x e ck z z 


or 

P„ (x, y, z, co) = 2 P n cos(0 n )e^ n 


-k x x-k y y-k z z) 


(3a) 

(3b) 


where x, yand zare evaluated on the surface and 
k x , k y and k z are evaluated at a particular angular 
frequency ox The pressure acting on the surface 
of each element, e, in the finite element model, 
due to the N plane waves, was computed using 
the x, y and z coordinates of the element center x e , 
y e and z e . The total pressure at the center of each 
element, P e , due to N incident plane waves is 


N 

P e (ox)= X2P„cos(0„)e 
n = 1 


+k x x e + k v y e + k z z e ) 


(4) 


where N is the number of plane waves used to 
approximate the diffuse field. This pressure 
distribution acting on the surface elements of the 
finite element model was used as an excitation. 
The velocity response of the finite element model 
was predicted due to the pressure excitation. The 
predicted velocities were imported into the 
boundary element model of the window and the 
transmitted sound power, n ( , was predicted. 

To compute transmission loss, the ratio of the 
incident to transmitted sound power is needed. 


— r P rosf/9 — — — 

l„ = CL LLJ— [sin( 9 n ) C0S ( y/ n ) i +8m(0„)sm(^„)./ + cos(0„)fc] 

pc 

(5) 

The intensity normal to the surface of the window 
is the z component of the intensity vector (Figure 
2). The sound power incident on a window of area 
A due to the n th plane wave is 

n,-,„ = AcosCfl, ) [P ” cos(0n )]2 (6) 

pc 

The total incident sound power for all N plane 
waves is 


N 

n,= sn,„ 

n = 1 


(7) 


The transmitted sound power is computed as 
outlined above. The predicted transmission loss 
of the window is computed from the ratio of the 
incident and transmitted sound power 


TL = 101og 10 



( 8 ) 


Results and Discussion 


Finite Element Model 

Concerns over stiffening effects associated with 
solid elements with high aspect ratios (length or 
width to thickness ratio) lead to a mesh refinement 
study. Mesh refinement for the solid (CHEXA) 
element model was based on comparison of a 
solid model with five elements through the 
thickness (60,2,114,2,60 window configuration) 
and plate models with uniform plexiglas material 
properties for all elements. A modal frequency 
response analysis for point force excitation from 
60 to 1000 Hz was used for comparison of the 
various models. For this study, 200 modes were 
included in the modal frequency response 
solution, which accounts for modes with 
frequencies through 4000 Hz. A 38x15 mesh 
(approximately 1 inch square element) was used 
as the baseline. Figure 7 shows the results of 
predictions for three different meshes of the solid 
model. As can be seen, there was a stiffening 


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effect for the 38x15 mesh but the results for the 
76x30 and 152x60 solid element mesh did not 
change significantly. The predictions for the76x30 
solid element mesh were also in excellent 
agreement with the plate model results. 
Therefore, a mesh of 76x30 solid elements was 
determined to be sufficient. 

In earlier work on the finite element analysis of 
damped structures, 10 ' 11 the viscoelastic layer was 
modeled with solid elements but the base and 
constraining layer were modeled with plate 
elements. Plate elements offer the advantage of a 
reduced number of degrees of freedom if the 
plates are defined on the surface of the solid 
elements with offsets used to account for the 
location of the mid-plane. A model using plate 
elements for the base and constraining layers for a 
175,2,60 layup with uniform plexiglas properties 
was compared to a uniform plate model. A 76x30 
element mesh was used. Figure 8 shows the 
results of a modal frequency response analysis. 
The plate-solid-plate model was consistent at 
lower frequencies but had a softening effect in the 
higher frequencies. This softening effect was not 
present in the solid models shown in Figure 7. 
Therefore, a solid model was used for all layers in 
subsequent analyses. 

Radiated Sound Power Prediction 

The measured and predicted sound power for a 
uniform plexiglas window and a damped plexiglas 
window are shown in Figures 9 and 10, 
respectively. Measured and predicted results are 
in good agreement. Discrepancies at the first 
resonant frequency are associated with a coupling 
of a window mode and a mode of the supporting 
fiberboard test fixture. The test fixture is not 
included in the finite element model and therefore 
its dynamic effects are not captured in the 
predicted results. Above 500 Hz, predictions 
have higher damping than the experiment but 
consistent trends in magnitude are observed. The 
predicted sound power for several damped 
plexiglas window layups are shown in Figure 11. 
Reductions in the radiated sound power of as 
much as 7 dB at some of the lower frequencies 
and 3.3 dB over the 1kHz bandwidth are 
demonstrated. These predicted reductions are 
consistent with experimental results shown 
previously in Figure 4. 

Parametric Study 

A parametric study was performed to examine the 
optimum placement of viscoelastic damping 
material within a nominally 0.25” thick plexiglas 


window. Utilizing test verified finite element 
models, windows with two and three plexiglas 
layers with viscoelastic damping material 
sandwiched between each layer were analyzed. 
The total amount of viscoelastic material was held 
constant for all of the window layups. The two 
layer windows used a single .004” thick 
viscoelastic layer while the three layer windows 
had two .002” thick viscoelastic layers. Figure 12 
shows the results of the parametric study. For a 
symmetric three-layer plexiglas window, the 
radiated sound power decreased as the center 
plexiglas layer thickness decreased and the 
optimum design converged to a window with two 
equal thickness plexiglas layers. Results for the 
two layer designs also showed the greatest 
reductions were obtained for two plexiglas layers 
of equal thickness with the viscoelastic material at 
the mid-plane. This is consistent with published 12 
panel damping design recommendations when the 
base and constraining layers are made of the 
same material. 

TL Prediction 

The 216 and the 60,2,114,2,60 window were 
studied. The measured change in the 
transmission loss caused by the addition of the 
constrained layer damping was computed from the 
measured transmission loss data shown in Figure 
5. The measured change in transmission loss is 
shown in Figure 13, red line. The change in 
transmission loss was most significant at the first 
resonance of the panel where an increase of 6 dB 
was observed. In the mass controlled region, an 
increase of 1 to 2 dB was observed in the 
transmission loss. Using the combined finite 
element, boundary element and diffuse acoustic 
field models, predictions of the transmission loss 
of the 216 and the 60,2,114,2,60 plexiglas 
windows were made. The predicted change in 
transmission loss was computed (Figure 13, green 
curve). There is good agreement between the 
measured and predicted change in transmission 
loss caused by the addition of the damping layer. 
In general, the predicted change in transmission 
loss is within 0.5 dB of the measurement (Figure 
13). The finite element model of the panel 
incorporating the modal frequency response 
solution was used. The damping loss factor and 
shear stiffness of the viscoelastic damping layer 
were assumed to be constant with respect to 
frequency. However, the properties of the 
viscoelastic damping layer used in the experiment 
varied with respect to frequency. The errors 
observed when comparing the measured and 
predicted change in transmission loss are likely 


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due to difficulty estimating the viscoelastic 
properties of the damping layer and variation of 
the viscoelastic properties with frequency. 

Summary and Conclusions 

Numerical modeling of plexiglas windows showed 
good agreement with experimental data. The 
60,2,114,2,60 window resulted in the best 
acoustical performance of the windows tested. 
The numerical models were used to determine the 
optimal damped plexiglas panel configuration. 
Based on a parametric study of two and three 
layer plexiglas windows with equal amounts of 
viscoelastic material, the optimum design 
converged to a window with two equal thickness 
plexiglas layers. These results show that it is most 
advantageous to place all of the damping material 
at the mid-plane where the shear strains are the 
largest. The modeling approach has been 
validated and can be used to evaluate other 
design configurations. Predicted reductions in the 
radiated sound power of as much as 7 dB at some 
of the lower frequencies and 3.3 dB over the 1kHz 
bandwidth demonstrate the potential of damped 
windows for noise control applications. 

The change in transmission loss caused by the 
constrained layer damping was predicted using a 
simulated diffuse acoustic excitation of the finite 
element model. There was good agreement 
between the measured and predicted change in 
transmission loss caused by incorporation of the 
viscoelastic damping layer in the window. This 
method can be used to study sound transmission 
properties of windows and other structures that 
incorporate constrained layer damping. 


Reference: 

1 . Pyper, J., “Laminated Glass Provides Noise 
Barrier Benefits in Automobile and 
Architectural Applications,” Sound and 
Vibration, August 2001 , pp. 10-16. 

2. Freeman, G. E., and Esposito, R. A., “Glazing 
for Vehicle Cabin Sound Reduction,” 
Proceedings of Inter-noise 2002, Detroit, 
Michigan. 

3. Lu, J., “Passenger Vehicle Interior Noise 
Reduction by Laminated Side Glass,” 
Proceedings of Inter-noise 2002, Detroit, 
Michigan. 


4. Lu, J., “Designing PVB Interlayer for 
Laminated Glass with Enhance Sound 
Reduction,” Proceedings of Inter-noise 2002, 
Detroit, Michigan. 

5. Gibbs G., R. Buehrle, J. Klos and S. Brown, 
2002, “Noise Transmission Characteristics of 
Damped Plexiglas Windows”, AIAA 2002- 
241 6 , Proceedings of the 8th AIAA/CEAS 
Aeroacoustics Conference, Breckenridge, 
Colorado, June 17-19,2002. 

6. Grosveld, F. W., “Calibration of the Structural 
Acoustic Loads and Transmission Facility at 
NASA Langley Research Center,” 
Proceedings of the Inter-noise 99, Fort 
Lauderdale, Florida. 

7. Klos, J., and S. A. Brown, 2002, “Automated 
transmission loss measurement in the 
Structural Acoustic Loads and Transmission 
facility at NASA Langley Research Center”, 
Proceedings of Inter-noise 2002, Detroit, 
Michigan. 

8. Lord, H. W., Gatley, W. S., and Evensen, H. 
A., Noise Control For Engineers, MCGraw- 
Hill, Inc., New York, 1980, pp.243 

9. Fahy, F., Sound and Structural Vibration: 
Radiation, Transmission and Response, 
London: Academic Press, 1995. 

10. Johnson, C.D., et.al., “Finite Element Design 
of Viscoelatically Damped Structures,” 
Proceedings of the AFWAL Vibration 
Damping Workshop, 1984 

1 1 . Kluesener, M. F., “Results of Finite Element 
Analysis of Damped Structures," Proceedings 
of the AFWAL Vibration Damping Workshop, 
1984 

12. Ungar, E. E., Damping of Panels, Chapter 6, 
Noise and Vibration Control, Edited by Leo L. 
Beranek, McGrawHill, Inc., 1971 


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Double Layer 


Triple Layer 


Plexiglas 

Damping » 



* Layer <7 






Figure 1 . Damped plexigas window configurations 




Figure 3. Plexiglas window installed in SALT TL window, view from reverberation chamber. 

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Figure 4. Measured radiated sound power for 
nominally Vi-inch thick windows installed in 
SALT. 



Figure 5. Measured transmission loss of the 
undamped “■ — ” and damped “ — ” windows. 



Figure 6: Plane wave incident on a Plexiglas window. The plane wave is shown propagating in the x-z 
plane, the y axis is into the page. The angle ^represents a rotation of the heading of the plane wave 
about the z axis. 


American Institute of Aeronautics and Astronautics 



Figure 7. Drive point frequency response functions for 
FEM mesh refinement study. 



and plate-solid-plate (dashed) models. 


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Figure 9. Measured and predicted radiated 
sound power for 21 6 panel. 



Figure 10. Measured and predicted radiated 
sound power for 1 14,2,1 14 panel. 



Figure 1 1 . Predicted radiated sound power for 
point force excitation. 



Figure 1 2. Results of parametric study showing 
the effect of window layup. 



Figure 13. Comparison of the change in 
transmission loss due to the constrained layer 
damping. 


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